Topology-Aware Joint Graph Filter and Edge Weight Identification for\n Network Processes

Data defined over a network have been successfully modelled by means of graph\nfilters. However, although in many scenarios the connectivity of the network is\nknown, e.g., smart grids, social networks, etc., the lack of well-defined\ninteraction weights hinders the ability to model the observed networked data\nusing graph filters. Therefore, in this paper, we focus on the joint\nidentification of coefficients and graph weights defining the graph filter that\nbest models the observed input/output network data. While these two problems\nhave been mostly addressed separately, we here propose an iterative method that\nexploits the knowledge of the support of the graph for the joint identification\nof graph filter coefficients and edge weights. We further show that our\niterative scheme guarantees a non-increasing cost at every iteration, ensuring\na globally-convergent behavior. Numerical experiments confirm the applicability\nof our proposed approach.\n